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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Trigonometric Equations

BITSAT 2009 · Mathematics · Trigonometric Equations

Period of ( ( θ+ 2 θ)/( θ+ 2 θ) ) is

Period of (sin⁡θ+sin⁡2θcos⁡θ+cos⁡2θ\frac{\sin \theta+\sin 2 \theta}{\cos \theta+\cos 2 \theta}) is

Options

  1. A(2 \pi)
  2. B(\pi)
  3. C(2π3\frac{2 \pi}{3})
  4. D(π3\frac{\pi}{3})

Correct answer

C. (2π3\frac{2 \pi}{3})

Step-by-step solution

sin⁡θ+sin⁡2θcos⁡θ+cos⁡2θ=2sin⁡(3θ2)cos⁡(θ2)2cos⁡(3θ2)cos⁡(θ2)=tan⁡(3θ2)Hence period =2π3\begin{aligned} & \frac{\sin \theta+\sin 2 \theta}{\cos \theta+\cos 2 \theta}=\frac{2 \sin \left(\frac{3 \theta}{2}\right) \cos \left(\frac{\theta}{2}\right)}{2 \cos \left(\frac{3 \theta}{2}\right) \cos \left(\frac{\theta}{2}\right)}=\tan \left(\frac{3 \theta}{2}\right) \\ & \text{Hence period }=\frac{2 \pi}{3} \end{aligned})$
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